Anyone here play Backgammon?

[MangoJ]

I've never played backgammon or chess seriously, but let's count the backgammon states:
(25^15 / 15!)^2 = 10^18
where 25^15 / 15! is the number of distributing 15 pieces to 25 different places (24 fields on the board, 1 in prison),square that for 2 players..

Whereas chess has roughly binom(64,8)*binom(56,8)*binom(54,2)*binom(52,2)*binom(50,2)*binom(48,2)*binom(46,2)*binom(44,2)*42*41*40*39 = 10^43
different states...

From the point of an exact strategy, where you want to evaluate every state and make the best move from all possible options, backgammon (at least in my naive view) is much "easier".

 

[BrianCP]

The number of possible states for the pieces to be in is smaller, but factor in 36 different possible rolls (30 for the opening state) some of which have decisions that are pretty much almost identical in expected value (calculated based on 3 different ways to win, win, gammon, backgammon, worth 1, 2, and 3 points respectively). A move that decreases your actual number of moves might actually be correct due to the increase in gammons and backgammons. Of course this doesn't even take into account proper use of the doubling cube (which offers to double the stakes of the match. If refused, the opponent loses the match at the current stakes. If he accepts, he gains complete control of the cube, allowing him to re double if the tide turns later on).

The actual positions are less in number, but there a lot of variables at play for each possible position. The correct play in a certain chess set up is always the correct play, the correct play in a backgammon position depends on the numbers you rolled and the different ways a win can count for extra points.

 

[FLASH1296]

My nickname here is Flash 1296 for a good reason.

In Backgammon a mere two rolls of the dice have 1,296 possibilities.

Players frequently determine the best move to make by multiplying the
number of my good (or bad) rolls with the same for my opponents rolls,
and dividing by 12.96 (rounded to 13) to compare the result.

There are 36 possible rolls of a pair of dice.
The 6 "doubles" (1-1, 2-2, 3-3, 4-4, 5-5, 6-6) appear once each
and all the rest appear twice each. e.g. 2-1 and 1-2 are the same.

So we start with 36 possible rolls.
The next roll brings that to 1,296.
The third roll makes that 4,6656.
The 4th roll (still just the opening sequences)
expands to 1,679.616 possibilities.
It does not take many more rolls before we have far
exceeded the number of atoms in the known universe.

All experienced backgammon players think (numerically) using
not a decimal system, but a system based on 36ths.
Each 36th = 2.78%

Here is a really simplistic example or two:

If I know that I can win by your throwing any Ace or Deuce that is odds of
20 of 36 rolls 2.8 x 20 = 56% = odds of 6 to 5

If I need to roll a 6 or a 5 or a total of 6 or 5 pips …

I can roll any 6 or 5 that is 20 combinations PLUS
5-1, 4-2, 3-3, 2-2, 4-1, 3-2. That is an additional 10 rolls
for a total of 30 out of 36 rolls. 2.8 x 30 = 83%
That equals odds of 5 to 1

Tonight, like every night, I will play a few tournaments
matches on-line. I can rest assured that I have played
unique matches that have never before occurred, Never!
Not in the last five millennia that backgammon has been played.

BG tournaments often include numerous mathematicians,physicists,
astrophysicists, computer scientists, and (especially) actuaries.

I once enjoyed playing against someone taking a few days off
from his 9 to 5 position, managing the Hubble Space Camera.

 

[Thunder]

Chess is a far simpler game than Backgammon.

Go is also a tougher game than chess.

Backgammon is a game whose complexity is so deep that Computer Neural Nets,
(having taught themselves to play with their powerful Artificial Intelligence), can
play much better than most people; but facing world-class tournament players they
are unable to play flawlessly.

Having been a good player in both games Flash, I respectfully disagree with your sentiments. Chess requires much deeper thinking imo and there is no luck involved. Backgammon on the other hand involves quite a bit of luck hence less thought process imo. Funny thing is, I'm rated a lot higher in backgammon than in chess.

 

[Katweezel]

I was just wondering if this forum happened to contain some backgammon players. Seems like there should be at least one....bunch of people that were alive in the 70's, lots of math nerds, people that gamble for a living.....all these add up to backgammon. I learned to play early last summer and occasionally go to a nearby club that meets once a week for a tournament.

Find out if there's a backgammon club near where you live. Join. It's fun, and you get to meet all kinds of people and players... Find out who's rated. Watch them play and ask them for tips. Play against them. Otherwise, find out when Flash and Thunder are next in town. :grin:

It's tough trying to learn this game from books. (Same goes for chess, blackjack, mahjong etc.) Nothing beats hands-on experience, especially with someone who knows what they are talking about. In this game, let's say there are ten skill levels, with novice at level one and Master at 10. If you get to level 5, you might beat a level 6 sometimes, but in the long run, 6 will prevail, and get your cash. Similarly, if you're up against a 9, you'll be skun and hung out to dry fairly quickly... and left to rue how unlucky you were.

BG was said to have been invented thousands of years ago by the Arabs, the Greeks, the Indians, the Chinese, the Israelis and the Aussies. :grin: Years ago, this game was thought to be 25% skill and 75% luck. Good luck... :grin:

 

[FLASH1296]

One of the ways that the compexity and (ultimate) difficulty of a game
can be measured is by how many levels of expertise are recognized.
In those terms, Go is the supreme leader of all games, bar none.
In Japan expert Go players are revered.

Chess is a memory game. It focuses upon being able to recall and project long series of plays. [So is tournament level Scrabble™]

Go is a spatial game. I cannot play a lick. I have no spatial sense.

Backgammon is a game centered upon complex probabilities.

Different games, like different sports, tap different abilities.

Experts are sometimes quoted as saying that there is a 20% luck factor in Backgammon. That may or may not be accurate, but it is nothing like the "luck factor" in Blackjack.

In blackjack one can have the True Count flatter you with big positive numbers,
it is not hard to lose every hand in a shoe; but over the long run we have
a nice positive expectation.

If I play a beginner a lengthy backgammon match, [e.g. 25 points], he has far less
than a 1% chance of beating me. 100 to 1 odds anybody ? :grin:

If that same beginner plays me a 1 point match, he has significant winning chances, perhaps even between 35% and 40%.

 

[Sucker]

Sucker, I figured you might go for that one...:grin:
Some years back, an experiment had a team of basketballers practising every day for hours for a week, throwing baskets. Their score average didn't change. Another team spent hours every day doing nothing except visualizing successfully throwing baskets. This team improved their average considerably.

Where I live there is a popular (English) football game called Rugby League. It's similar to Gridiron, with similar goalposts. A try (touchdown) must be successfully converted with an unhurried kick, for the extra two points. Most of these kickers are using visualization for ten or more seconds before the attempt... Do not degrade the power of the viz...

Double five is one chance in 36. No problem! It's a cinch... :laugh:

This is what's known as psychocybernetics, and of COURSE it works. It has been conclusively proven over and over again. Dr. Maxwell Maltz wrote a VERY good best-seller book by the same name; on that subject - back about 30-40 years ago.

But the DICE trick that you're talking about is psychokinesis (also known as telekinesis), the so-called ability to move objects through mind control alone. Psychokinesis is a COMPLETELY unproven "science" that has never ONCE throughout history been successfully demonstrated to actually WORK.

Please don't confuse the science of psychocybernetics with the hogwash of psychokinesis. Or if you insist, at least move it to the "voodoo" section, where it belongs.

Believe me when I tell you how much I WISH psychokinesis was possible. I would work one day a month. Imagine betting $100k on a baccarat hand, and visualizing your side getting a natural nine! :grin:

 

[MangoJ]

My nickname here is Flash 1296 for a good reason.

In Backgammon a mere two rolls of the dice have 1,296 possibilities.

Players frequently determine the best move to make by multiplying the
number of my good (or bad) rolls with the same for my opponents rolls,
and dividing by 12.96 (rounded to 13) to compare the result.

There are 36 possible rolls of a pair of dice.
The 6 "doubles" (1-1, 2-2, 3-3, 4-4, 5-5, 6-6) appear once each
and all the rest appear twice each. e.g. 2-1 and 1-2 are the same.

So we start with 36 possible rolls.
The next roll brings that to 1,296.
The third roll makes that 4,6656.
The 4th roll (still just the opening sequences)
expands to 1,679.616 possibilities.

Two dices have only 6*5/2+6 = 21 possible rolls. But that's not the problem. The figures above doesn't make any sense, that are just the number of possible games on 4 rolls. Surely they do explode. But this is not the complexity one needs to handle. Playing the game is a lot "easier" than running through all possible games.

Compare this to Blackjack (from an infinite shoe - so no counting). What is the number of different games like? something like 13^4..6. But that doesn't matter. What matters is the number of different states of the game, which is your hand and the dealers upcard. and this is just 41*10 = 410. If you evaluate those 410 states correctly, you have solved the game. The solution to this game is called basic strategy.

Backgammon is the same: The number of possible games is not important, the number of states is. How to evaluate ? That's simple, start from the back of the game, i.e. all winning positions, and assign an EV of 1,2,3 (for single, gammon, backgammon). From all those positions, make all possible moves backward, and assign/sum the EV with the probability of rolling the corresponding dice pair. Then move back further, untill you reach the start configuration.
With this you have a "basic strategy" for backgammon. The Doubling cube is then simple to handle: Offer the cube whenever your EV is above 0.5.
Decline the cube whenever your EV is below -0.5.

The only difficulty is the large number of states (10^18). You don't need the number of games, because it doesn't matter on which specific way the game evolved to it's current state. The backgammon board (or the dices) have no memory.
But this is by no means comparable to chess, where even the number of states is a lot larger (10^30), or even Go (3^(19^2) = 10^172).

 

[FLASH1296]

There are 6 faces on a die and when you roll 2 of them there will be 36
possible outcomes. The fact that the rolls of "doubles" only appear one way
each is taken into consideration of course. 36^36=1296

You said: "But this is not the complexity one needs to handle. Playing the game
is a lot "easier" than running through all possible games. "But this is not the
complexity
one needs to handle. Playing the game is a lot "easier" than running through all possible games."

This is the same as in chess, where there are only a few opening moves and
there are many standard popular opening sequences and defenses, e.g. Sicilian.

All solid chess players memorize long sequences of moves.

Final Note:

My point is that computer play whips expert human play in Chess, but not in Backgammon, or No Limit Texas Hold Em.

 

[BrianCP]

or No Limit Texas Hold Em[/FONT].

I think if a computer was allowed to observe a play for a large number of hands before playing them, they could probably adopt a maximally exploitive strategy quite easily based on their statistics. The Mathematics of Poker goes into how the math has much more to do with ranges and statistics, so in theory, you could make a program that adapts to a particular opponent with the information presented to it quite well.

 

[MangoJ]

Flash, I didn't want to say that Backgammon is "easy to play". I just wanted to say that the process of solving Backgammon is rather "easy" in principle and highly straightforward. However due to lack of ressources, other (highly sophisticated but in a strict sense sub-optimal) strategies have to be created - and this is where things get messy and really difficult.

I'm not sure if there is an optimal strategy for poker (because both players have different kind of information), though. It could be that strategy A beats strategy B, and strategy B beats strategy C, and strategy C beats strategy A.
Hence knowing the strategy of your opponent has far greater value than on full-information games (simply choose C when your opponents uses A).

 

[BrianCP]

Optimal strategy for poker is whatever play will win the most money from a particular opponent given their style of play.

 

[Sucker]

FWIW: Among other things, Bill Robertie is a former world-champion backgammon player, and he's ALSO a former world-champion in speed chess. He tells me that backgammon is 10 times harder than chess.

 

[FLASH1296]

Robertie is not the only chess champion who has stated this. It is a consensus opinion.

Bill Robertie is the only two-time World Champion of Backgammon; and is
an indefatigable writer of influential books on BG strategy, studied by all
serious players.

A very fine book was published by a Philadelphia based expert player - the sole subject
matter of which was the published errors made by Robertie in one of his best books.

Such is the world of backgammon, where no human being can play virtually perfect "BG."
Gary Kasparov's play at chess is as close to perfection as one can conceive of.

 

[Lonesome Gambler]

I think if a computer was allowed to observe a play for a large number of hands before playing them, they could probably adopt a maximally exploitive strategy quite easily based on their statistics. The Mathematics of Poker goes into how the math has much more to do with ranges and statistics, so in theory, you could make a program that adapts to a particular opponent with the information presented to it quite well.

This would only be true if the person being played against wasn't aware of the computer's data gathering (ie. level 2 thinking, and nothing above that). A computer playing optimally against statistical tendencies wouldn't necessarily do much better than a very skilled player with extensive HUD stats. A world-class player would understand how to manipulate the computer's perception of their possible ranges based on awareness of their own observed tendencies. This is the whole theory behind balancing ranges vs. thinking opponents.